1. Field of the Invention
The present invention relates generally to gear tooth configurations, and more specifically to various gear tooth profiles having a non-involute shape to provide conformal contact between adjacent teeth. The present invention relieves the compressive forces between convex to convex contact of mating gear teeth, by means of a relief formed in one or both of the faces off the mating teeth.
2. Description of the Related Art
Power transmission through gears and/or racks, was first developed hundreds of years ago with simple wooden dowel and socket devices. It was recognized that such relatively crude power transmission systems were not particularly efficient or durable, but it was not until metallurgy and machining was better developed that more efficient gear systems were developed.
It was soon recognized that the specific shape or profile of the teeth of gears, has a considerable bearing upon the accuracy of movement of the gear train, the friction of the gear train, and also the durability of the gears. Various geometric forms have been used for shaping gear teeth, generally based upon the generation of a locus of points along a line being rotated along or generated from the rotation of a circle.
Two basic tooth shapes or profiles have received by far the greatest development: The cycloid, and the involute. The cycloid refers to a curve generated by a point on a circle which is in turn rolled along a straight line. The involute profile is generated by a point on a line which is unrolled from a circle. Both curves are of constant convex shape, with the involute having a constantly increasing radius. Accordingly, these profiles, particularly the, cycloid series, have been modified in the past to provide composite shapes having concave dedenda (the portion below the pitch circle) and convex addenda (above the pitch circle), and/or using a larger hypocycloid to generate a larger base radius for the dedendum of the tooth, relative to a smaller radius for the addendum.
Such a cycloidal (i. e., non-involute) profile possesses a number of advantages over the involute shape, but it was generally not possible to make beneficial use of these advantages until modern times and the development of more sophisticated machining technology. As a result, the involute gear tooth profile has been favored for a long period of time, as (1) it was easier to manufacture; (2) center-to-center distance between shafts is not as critical; and (3) transmission of motion is more uniform with the involute gear profile. Both the cycloid and involute profiles, as well as others, result in relatively high compressive stress concentrations at the area of contact with adjacent teeth where non-conformal (i. e., convex to convex) gear tooth profiles are used, and also in the areas where curvature reverses direction.
However, the cycloid tooth profile does enjoy at least one advantage over the involute profile, in that it is generally a more efficient shape for transmitting force from one gear tooth to an adjacent tooth. Nonetheless, the cycloid profile has not found great favor for the various reasons noted above, even though at least some of those reasons are no longer valid with modern machining technology. While one reason for the lack of acceptance of the cycloid profile may be simple human inertia, in that the involute gear profile has been in widespread use for decades, another reason is the relatively high compressive stress concentration of the cycloid profile at about the pitch circle of the gear.
Accordingly, the present invention provides a means of relieving the relatively high compressive stress which would otherwise occur in the general center of a cycloid (or more generally, non-involute) gear profile where the gears have conformal contact, i. e., generally congruent mating surfaces to provide area contact rather than contact along a relatively narrow line across the face of the tooth. The present invention provides a physical relief formed in the faces and flanks of the gear teeth at the area of each tooth where stresses would otherwise be highest (the face of a gear tooth is the surface of the gear tooth above the pitch circle, while the flank is the surface of the gear tooth below the pitch circle). The use of non-involute gear tooth profiles greatly reduces sliding contact between adjacent gear teeth, while the relief area of the tooth profile serves to eliminate the high compressive forces which would otherwise occur between the convex to convex mating surfaces of such non-involute tooth profiles. Smooth operation is provided by means of helical gear sets which provide tooth profile contact ratios of two or better, in order to avoid rotational discontinuity due to the tooth face relief areas.
A discussion of the related art of which the present inventor is aware, and its differences and distinctions from the present invention, is provided below.
U.S. Pat. No. 1,613,702 issued on Jan. 11, 1927 to Sigard A. S. Hammar, titled “Gear Tooth,” describes a tooth profile having a series of steps formed therein. Hammar states that his gear tooth profile provides the strength benefits of the ideal parabolic shape, while also providing tooth profiles between each step which are optimized for relatively high efficiency and low frictional losses. It is noted that the gear tooth profiles illustrated in the drawings of the Hammar '702 U.S. Patent are convex, with the exception of the steps along each tooth. However, Hammar makes no suggestion of any means for relieving the relatively high compressive loads which occur between mutually convex surfaces of mating gear teeth, as provided by the present invention.
U.S. Pat. No. 1,646,374 issued on Oct. 18, 1927 to John T. Wilkin, titled “Gear,” describes a gear configuration having a relatively tall and narrow profile. While such gear profiles do not possess particularly high strength per se, Wilkin configures his gear profiles so that a series of several teeth are engaged simultaneously between the driving and driven gears. This results in the bending stresses on each tooth being relatively low for a given torque being applied from the driving to the driven gear. However, the Wilkin gears, due to their relative length and multiple tooth engagement, result in considerable sliding contact between teeth in the approach and departure areas of mesh. Also, while Wilkin configures his gear teeth with relatively wider addendum portions in order to provide the desired multiple tooth engagement, he does not provide any form of relief in these convex areas to preclude high compressive forces between the end of one tooth and the convex addendum area of the adjacent tooth.
U.S. Pat. No. 2,335,504 issued on Nov. 30, 1943 to Antoine Gazda, titled “Gear Teeth,” describes the provision of slots extending from the outer end of each tooth, inwardly toward| its root. Gazda's object is to allow the teeth to flex somewhat more than otherwise, in order to provide some resilience upon engagement and thus provide quieter operation and reduce cracking and breakage at the root due to the relatively brittle structure of a conventional gear tooth. Gazda does not disclose any means for reducing the high compressive forces occurring between convex faces of mating teeth, as provided by the present invention.
U.S. Pat. No. 3,533,300 issued on Oct. 13, 1970 to Robert M. Studer, titled “Helical Gearing,” describes a variation in Novikov type gear profiles incorporating circular arcs for the profiles. The Studer gear profile uses a double flank shape, having a convex addendum and concave dedendum to produce a somewhat sinusoidal tooth profile from root to tip. However, Studer widens the concave dedendum portion in order to provide greater bending strength for the resulting relatively tall tooth. This results in a generally horizontal step (i. e., generally parallel to the pitch circle) between the concave and convex portions of each tooth face. The gear profile of the Studer '300 U.S. Patent thus more closely resembles the profile of the Hammar '702 U.S. Patent, than the gear tooth profiles of the present invention. A review of FIG. 2 of the Studer U.S. Patent shows that substantially all of each tooth face contacts the adjacent tooth face as the gears roll through mesh, whereas the present gear profile results in a relief formed generally to each side of the pitch circle, with the relief area remaining out of contact with the adjacent gear tooth face.
U.S. Pat. No. 4,184,380 issued on Jan. 22, 1980 to Evgeny I. Rivin, titled “Gears Having Resilient Coatings,” describes an elastomer coating upon at least one face of the teeth of one of a meshing pair of gears. Rivin states that this reduces friction and noise, as the elastomer compensates for the sliding which would otherwise occur between gear teeth. The Rivin coating does not provide a relief in the tooth profile to relieve contact pressure between mating convex areas of the gear teeth.
U.S. Pat. No. 4,238,970 issued on Dec. 16, 1980 to Willis M. Carter, titled “Bevolute Gear System,” describes a ring and pinion gear assembly in which the tooth pattern (but not necessarily the profiles of the individual teeth) is an involute curve for both the ring and the pinion. While Carter states that this pattern may be applied to ring and pinion sets using many different types of gear tooth profiles, he does not disclose any relief in the faces of his gear teeth for relieving high contact pressures across those mating areas of the teeth, as provided by the present non-involute gear profile invention.
U.S. Pat. No. 4,367,058 issued on Jan. 4, 1983 to Willis M. Carter, titled “Bevolute Gear System,” is a divisional patent of the '970 U.S. Patent discussed immediately above. The same points of distinction between that patent and the present invention, are; seen to apply here as well.
U.S. Pat. No. 4,640,149 issued on Feb. 3, 1987 to Raymond Drago, titled “High Profile Contact Ratio, Non-Involute Gear Tooth Form And Method,” describes a gear tooth profile which combines involute and non-involute profiles to provide a relatively high contact ratio for the meshing gears. It is noted that the resulting profile of the Drago gear, is essentially continuously convex, excepting the root area. This results in non-conformal contact across the entire tooth face, with resulting relatively high contact pressures. However, Drago does not provide any means for relieving the profile to relieve such high contact pressures, as provided by the present invention.
U.S. Pat. No. 4,653,340 issued on Mar. 31, 1987 to Joseph LaBate, titled “Beveled Spur Gear,” describes spur gear sets having beveled tips, so that when such gears are disengaged and then reengaged, the beveled tips slide circumferentially about one another to permit positive engagement of the teeth, rather than having the top lands of the teeth abut against one another. LaBate does not describe any particular gear tooth profile in his patent, other than describing the beveled tips of the teeth. No means is disclosed for relieving contact pressure in convex to convex gear tooth profiles, as provided by the present invention.
U.S. Pat. No. 4,911,032 issued on Mar. 27, 1990 to Ronald J. Steele et al., titled “One-Way Gear,” describes a gear profile in which a portion of one face of every second tooth is partially cut away, with the root retaining the original thickness. This results in a step formed somewhat below the pitch circle of every other tooth, on one side of those teeth. Such a gear can be used to drive another gear by means of the unstepped sides of the teeth, but if rotation is reversed, one of the steps of the stepped teeth engages a corresponding top land of a gear tooth of the driven gear, resulting in gear lockup. The Steele et al. gear profile has very limited application, due to the relatively large backlash from cutting away a portion of some of the teeth, and the relatively low contact ratio provided. Steele et al. do not provide any means of reducing the contact pressure applied between two adjacent convex gear tooth surfaces, as is accomplished by the present invention.
U.S. Pat. No. 5,271,289 issued on Dec. 21, 1993 to Meriwether L. Baxter, Jr., titled “Non-Involute Gear,” describes a series of gear tooth profiles providing conjugate operation between gears, i. e., constant rotational velocity being transmitted from the drive gear to the driven gear. Baxter, Jr. accomplishes this by varying the radius of the tooth profile between root and tip or outer land, with the increase and decrease in radius being generally symmetrical about the pitch circle. As the Baxter, Jr. gear tooth profile is a continually convex curve, albeit one of varying radius, it results in relatively high contact pressures along the contact areas of adjacent gear teeth. Baxter, Jr. does not disclose any means of relieving the high contact pressures between gear teeth, as provided by the present invention.
U.S. Pat. No. 6,178,840 issued on Jan. 30, 2001 to John R. Colbourne et al., titled “Gear Form Constructions,” describes gear profiles where the teeth of the first gear have a constant (or nearly so) convex curvature, with the teeth of the mating second gear having a mating concave curvature. Colbourne et al. state that their profiles provide conjugate operation without need for helical gears. However, the conformal contact (i. e., congruent surfaces resulting in area contact, rather than a line across the mating teeth) result in relatively high sliding velocities between the mating teeth, where they are not aligned with the pitch circle. While the Colbourne et al. gear tooth profiles result in reduction of high contact pressures due to their conformal shapes, no means is provided for relieving such forces along the center of the teeth.
U.S. Pat. No. 6,205,879 issued on Mar. 27, 2001 to Faydor L. Litvin et al., titled “Helical And Spur Gear Drive With Double Crowned Pinion Tooth Surfaces And Conjugated Gear Tooth Surfaces,” describes gear tooth profiles having compound convex curvatures of their contact faces. The stated advantage is that the actual contact areas of mating gear teeth form relatively wide elliptical patterns, due to the compression of the gear material upon contact. The Litvin et al. gear tooth profiles teach away from the profiles of the present invention, as the Litvin et al. profiles are continuously convex in two mutually normal planes over the tooth contact area. In contrast, the gear tooth profiles of the present invention include at least one concave relief formed generally at about the area of the pitch circle of each gear tooth face, thus removing all contact pressure from that area.
British Patent Publication No. 186,436 accepted on Oct. 2, 1922 to Francis J. Bostock et al., titled “Improvements In And Relating To Gear Teeth,” describes a gear tooth profile formed by combining aspects of the cycloid and involute curves. Bostock et al. claim various advantages from such a gear tooth profile, including ease of manufacture, low specific sliding, “enveloping” tooth profiles (this appears to refer to conformal contact, where the driving and driven teeth are shaped differently), relatively strong teeth, and low obliquity of the drive angle between teeth. However, the Bostock et al. gear tooth profile is a consistently curved surface, with no additional concave relief formed therein to relieve high contact pressures, as provided by the present invention.
British Patent Publication No. 1,232,019 published on May 19, 1971 to Robert M. Studer, titled “Improvements In Helical Gearing,” is the parent application to U.S. Pat. No. 3,533,300 to the same inventor, discussed further above. The '300 U.S. Patent and '019 British Patent Publication both describe a variation in Novikov type gear profiles incorporating circular arcs for the profiles. Studer provides a step in the sides of his gear teeth between the addendum and dedendum, citing improved bending and shear strength provided by the relatively wider bases of the stepped teeth. The same points raised further above in the discussion of the '300 U.S. Patent, are seen to apply here as well.
PCT Patent Publication No. WO 88/03,623 published on May 19, 1988, titled “Gear Drive With Mixed-Type Meshing,” describe (according to the drawings and the English abstract) a hybrid gear tooth profile having a convex involute shape at about the location of the pitch circle, with Novikov profiles extending thereabove and therebelow. The result is a somewhat sinusoidal tooth profile, with mating teeth bearing against one another along their mutual convex involute portions during at least part of their mesh. No relief area is provided along this convex portion of the profile to relieve the extremely high contact pressures occurring, as provided by the present gear tooth profile invention.
Section Two of the publication Manual Of Gear Design, original copyright 1935 (renewed 1962) by Earle Buckingham, provides a background discussion of various gear configurations and the mathematics and engineering involved in the selection and design of various types and configurations of gear teeth for various purposes. This publication notes the use of the accepted standard ASA-B6b-1933 of the AGMA (American Gear Manufacturers Association) and on p. 45, provides a discussion of proportions for a 14.5 degree composite gear system based upon the above noted ASA-B6b-1933 standard. While the present invention utilizes non-involute gear profiles including an at least partially cycloidal profile over a portion of the tooth face, Buckingham does not suggest any form of relief disposed in the face of the gear teeth in order to avoid high compression stresses, as provided by the present invention.
The book Analytical Mechanics Of Gears, copyright 1949 by Earle Buckingham (republished 1988 by Dover Publications Inc., New York), provides considerable information on gear profile theory and practice for virtually any type of gear (spur, helical, worm drive, etc.). Pages 25-29 discuss the cycloid, epicycloid, and hypocycloid shapes which may be used in forming gear tooth profiles, with the first portion of chapter two on pages 58-73 providing a discussion of the theory of the involute curve used in gear tooth profile formation. While other sections of the books deal with various other aspects of gear tooth profile theory, Buckingham does not disclose any provision for a relief formed generally in the central area of the tooth profile for relieving the otherwise high stress which would occur between mating convex surfaces of either involute or non-involute gear teeth.
A technical paper titled “On Design And Performance Of Involute-Cycloid Composite Tooth Profile Gear,” by Yoshio Terauchi et al., published as pp. 118-126 in the Bulletin of the JSME (Japanese Society of Mechanical Engineers) No. 199 (January, 1982) discusses the development of an involute-cycloid composite gear tooth profile to avoid the high compression stresses developed in the conventional continuously convex profiles of mating involute gear teeth. The last sentence of the first full paragraph of the second column of the first page (p. 118), notes that gears having cycloid curve tooth profiles are not suitable for transmitting loads, as the radius of curvature of the tooth surface is essentially zero at the pitch point. However, Terauchi et al. do not provide a relief across this area of the gear tooth to relieve the high contact stresses, as provided by the present invention.
A technical paper titled “Influence Of The Path Of Contact Shape On Sliding Conditions Between Tooth Flanks,” by Joze Hlebanja, presented at the JSME International Conference On Motion And Powertrains in Hiroshima, Japan, Nov. 23-26, 1991, describes research relating to the relative sliding velocities between different gear tooth profiles, and the effect upon the oil film between the gear teeth. While several different gear tooth profiles are considered, emphasis is placed upon a non-involute shape having a sinusoidal profile. While Hlebanja finds that such a profile provides benefits in maintaining the oil film between gear teeth, he does not disclose any provision for a relief formed in the tooth flanks for relieving high pressures between gear teeth.
Finally, another technical paper by Joze Hlebanja, titled “Main Advantages Of Non-Involute Spur Gears: The Design Of Non-Involute Spur Gears To Improve The Condition Of Contact,” copyright 1992 by the American Gear Manufacturers Association, provides a discussion of the use of different gear tooth profiles to affect the line of action (i. e., the movement of the contact position along the gear tooth between the root and tip as the gear teeth rotate through mesh) and how this affects the maintenance of the oil film between gear teeth. This paper is similar to the 1991 JSME paper discussed above, and as in that paper, no disclosure is made of any form of relief along the convex areas of the gear tooth profile to relieve high pressures in those areas.
None of the above inventions and patents, taken either singularly or in combination, is seen to describe the instant invention as claimed. Thus a non-involute gear configuration with conformal contact solving the aforementioned problems are desired.